The Regularity of the Value Function of Repeated Games with Switching Costs

Yevgeny Tsodikovich (1, 2) , Xavier Venel (3) , Anna Zseleva (4)

1 AMSE - Aix-Marseille Sciences Economiques
2 Bar-Ilan University [Israël]
3 LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]
4 Department of Quantitative Economics, School of Business and Economics, Maastricht University

We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In particular, the strategies exhibit a robustness property and typically do not change with a small perturbation of this ratio. Our analysis extends partially to the case where the players are limited to simpler strategies that are history independent―namely, static strategies. In this case, we also characterize the (minimax) value and the strategies for obtaining it.

Mots clés: Zero-sum games; Switching Costs; Repeated Games; Stochastic Games

Domaines: Economies et finances; Mathématiques [math]

Yevgeny Tsodikovich, Xavier Venel, Anna Zseleva. The Regularity of the Value Function of Repeated Games with Switching Costs. Mathematics of Operations Research, In press, ⟨10.1287/moor.2022.1325⟩. ⟨hal-03868995v2⟩